Motivated by the approximate inverse proposed by [1]} for the Fisher information matrix in the
directed one-mode network model involved with the bi-degree sequence, we proposed a generalized simple matrix \(S=(s_{i,j})\)  to approximate the \(V^{-1}\) , which is defined as
\(s_{i,j}=\left\lbrace \begin{array}{ll}\frac{\delta _{i,j}}{v_{i,i}}+\frac{1}{v_{m+n,m+n}}, & {i,j=1,\dots ,m,} \\-\frac{1}{v_{m+n,m+n}}, & {i=1,\dots ,m,~j=m+1,\dots ,m+n-1,} \\-\frac{1}{v_{m+n,m+n}}, & {i=m+1,\dots ,m+n-1,j=1,\dots ,m,}\\\frac{\delta _{i,j}}{v_{i,i}}+\frac{1}{v_{m+n,m+n}}, & {i,j=m+1,\dots ,m+n-1,}\end{array}\right.\) 
